Synthesize control for an SIR model with nonlinear saturation infecctious force

This paper is concerned with the Synthesize control of SIR epidemics model with nonlinear saturation infectious force, which not only isolate infective, but also take immunization and improve the sense of self-protection. The threshold of the models system is analyzed. In order to calculate the optimal values of the isolate rates, immune rates and self- protection rates, it constructs a performance index that is calculated explicitly as an algebraic function of the controller parameters by solving Zubov´s partial differential equation, and standard optimization techniques are employed. The ultimate aim is to eliminate the disease. The simulation result shows the method is viable and effectively.